However, for a third straight day, foul Scottish weather forced the alteration of plans from tournament officials.
While the fourth and final round was to have begun after the concluding third, weather delays halted play in the morning and made the continuation of golf impossible in the afternoon.
As a result, the top-60 pros and 20 leading amateurs will now play their final rounds on Monday at St. Andrews.
While the wet and cold conditions may have dampened some spirits Sunday, Lawrie did not seem to be affected at all.
The 1999 British Open champion picked up his third round at the Old Courses 13th hole, already 8-under thanks to Saturdays stupendous play.
He continued his fine golf, recording birdies at Nos. 14 and 15 to move to 15-under for the event, but bogeyed the par-4 16th to end in 63 for the day.
Nevertheless, his score has him in prime position for the record first-place prize of approximately $800,000, not to mention his first win since taking that Claret Jug in 99 at Carnoustie.
Click Here to see Paul Lawrie's scorecard.
Im pleased with that obviously but it was nice to see a few putts going in for a change, said Lawrie. Ive played will all year but Ive struggled on the greens. My season has been about regularly taking 33 or 34 putts for 71 or 72.
The Scottish native required just 27 strokes with the flat stick in his third round.
Likewise, continuing his solid golf was McGinley.
Picking up his round at Carnousties par-5 12th, the Irishman carded a solid birdie and parred his way in to a 1-under 71 to end tied for first.
However, while the two players sit on top entering the final day, the biggest threat may come from third-placed Ernie Els.
Just one shot back at 13-under, the South African capped off a 68 at St. Andrews on Sunday. He is searching for his first win of the year.
Also in the hunt is David Howell, who sits two off the pace at 12-under, while highly-touted rookie Paul Casey rattled home a 66 at St. Andrews to end in joint fifth with Brian Davis.
The final round is scheduled to begin at 9:00am local time on Monday.
Click Here for Full Field Scores from the Dunhill Links Championship.